On the dispersionless Davey-Stewartson system: Hamiltonian vector field Lax pair and relevant nonlinear Riemann-Hilbert problem for dDS-II system
DOI10.1007/s11005-019-01224-5zbMath1437.37085arXiv1809.04225OpenAlexW3106056580MaRDI QIDQ2300926
Publication date: 28 February 2020
Published in: Letters in Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1809.04225
Davey-Stewartson systemnonlinear Riemann-Hilbert problemdispersionless systemheavenly type equationsvector fields Lax pair
Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Stationary Riemannian space-times with self-dual curvature
- Inverse scattering transform method and soliton solutions for Davey- Stewartson II equation
- Recursion operators and bi-Hamiltonian structures in multidimensions. II
- Inverse scattering problem for vector fields and the Cauchy problem for the heavenly equation
- Recursion operators and bi-Hamiltonian structures in multidimensions. I
- Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
- On universality of critical behavior in the focusing nonlinear Schrödinger equation, elliptic umbilic catastrophe and the Tritronquée solution to the Painlevé-I equation
- Integrable structure of the Dirichlet boundary problem in multiply-connected domains
- Numerical study of the semiclassical limit of the Davey–Stewartson II equations
- Three-dimensional inverse scattering for the wave equation with variable speed: near-field formulae using point sources
- The dispersionless 2D Toda equation: dressing, Cauchy problem, longtime behaviour, implicit solutions and wave breaking
- On the solutions of the second heavenly and Pavlov equations
- Minitwistor spaces and Einstein-Weyl spaces
- On the infinite-dimensional symmetry group of the Davey–Stewartson equations
- Singularity-structure analysis and Hirota's bilinearisation of the Davey-Stewartson equation
- Two-dimensional lumps in nonlinear dispersive systems
- Killing vectors in self-dual, Euclidean Einstein spaces
- On the soliton solutions of the Davey-Stewartson equation for long waves
- The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
- Einstein-Weyl spaces and SU(∞) Toda fields
- Infinite-dimensional symmetry algebras and an infinite number of conserved quantities of the (2+1)-dimensional Davey–Stewartson equation
- Method for Solving the Korteweg-deVries Equation
- Anti-self-dual four–manifolds with a parallel real spinor
- On three-dimensional packets of surface waves
- A Study of the Direct Spectral Transform for the Defocusing Davey‐Stewartson II Equation the Semiclassical Limit
- The inverse spectral transform for the Dunajski hierarchy and some of its reductions: I. Cauchy problem and longtime behavior of solutions
- Quasiclassical generalized Weierstrass representation and dispersionless DS equation
- On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking
- Integrals of nonlinear equations of evolution and solitary waves
- Conformal maps and integrable hierarchies
